3d multilateration with unknown, but proportional, distances

I am trying to position a digital unit using a number of receivers by recording the signal strength at each receiver.

However, since not all digital units will emit with the same signal strength I cannot use the traditional approaches to multilateration (that I've heard of at least).

Could someone help me do this?

I've tried by considering the signal strengths [RSSI] as proportional to one another and subsequently tried to project them onto a coordinate system [m] - but just can't seem to get it right.

EDIT:

Essentially I want to reformulate this problem:

FIND coordinates of P

Given:

coordinates of receivers/nodes A,B,C in a 2D-plane : {x_A,y_A,...,y_C} [unit: m]

signal strength received at the nodes from unknown point P: {|RSSI_AP|,...,|RSSI_CP|}

Into this problem (that is easily solved using a trilateration algorithm):

FIND coordinates of P

GIVEN:

coordinates of receivers/nodes A,B,C in a 2D-plane : {x_A,y_A,...,y_C} [unit: m]

distance to point P from the receivers: {d_AP,d_BP,d_CP}

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